A 30-year bull run for bonds has finally come an end, according to Martin Gilbert, CEO of Aberdeen Asset Management, who told CNBC that the outflows seen in the market presents a buying opportunity.

"People feel we are nearing the end of this great bull market that we've had and really entering a bear market...people are trying to, I suppose, adjust for a change," he told CNBC Monday. "June was almost a turning point I think especially in fixed income."

Gilbert - whose company mainly deals in Asian and emerging market equities - said that the bond market is "bumping along the bottom", and the firm saw large outflows in June especially in fixed interest. The outflows have been self-inflicted rather than market-driven, he said.

The global sell-off in bonds began on May 22 after the minutes of the Federal Reserve's policy meeting signaled that its bond-buying program—which has boosted global bond prices—could soon be pared back. Fed "taper" fears have also meant that money has flowed back into the U.S. This has had negative effects on emerging market equities and currencies which have seen price drops. Societe General even declared in a research note at the end of May that the emerging market bull run is over.

"You just have to weather the storm, in fact it's a great buying opportunity actually. If you can have that discipline to buy at the bottom rather than sort of buy at the top," he said.